The issue of justice arises when there is a central authority, whether this authority takes the form of external abstract (political/legal government) or authority that takes the form of an internal abstract (the mind) where the law of kamma operates.
Both can be used skillfully by being consciously biased using non-harming as a guiding principle. For example, using law of Kamma to interpret reality at the individual level prevents the individual from engaging in harmful behavior by assuming himself responsible (heir of) his actions. The same non-harming principle would prevent him from translating individual responsibility of others to meriting/justifying their suffering (using worldly belief system skillfully). A theory has an explanatory power, but that does not mean it justifies the status quo as the same theory is meant to change reality in a way that is conducive to human well-being.
More generally, any law that utilizes reward and punishment for making people behave seems to be conducive to greed and fear as the main drivers for human behavior. This is why Kamma (both white and black) is described by the lord Buddha as suffering.